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Groups > sci.math > #416035 > unrolled thread
| Started by | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| First post | 2018-06-22 07:36 -0700 |
| Last post | 2018-07-05 14:08 +0200 |
| Articles | 20 on this page of 638 — 20 participants |
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In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 07:36 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-22 07:46 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 08:00 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 08:07 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 08:12 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 08:21 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-22 08:33 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-22 08:05 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 08:50 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-22 09:26 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 09:36 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-22 09:41 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 09:49 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-22 10:16 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-22 10:23 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 11:43 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-22 12:07 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-23 03:11 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-23 06:10 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 13:11 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-22 13:19 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-23 03:11 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-23 04:55 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-23 05:01 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-23 06:40 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-23 07:10 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-23 07:13 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-22 18:47 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-23 03:11 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-23 07:32 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-23 06:19 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-24 09:26 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-24 07:44 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-24 08:00 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-24 08:05 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-24 08:14 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-24 08:27 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-24 08:36 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-24 09:00 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-25 20:46 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-26 04:10 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-26 13:34 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 13:38 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-26 14:01 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 14:14 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 14:23 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 14:26 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-26 14:38 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 15:24 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 15:28 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 15:33 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 15:51 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 15:59 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 16:09 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 16:23 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 16:29 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 16:35 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 16:47 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 16:51 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 16:53 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 17:01 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 17:14 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 17:20 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 17:27 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 17:29 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 17:35 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 17:39 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 17:52 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 19:02 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 19:33 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-27 00:58 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-27 01:03 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-27 06:54 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 17:19 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-26 20:48 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 21:13 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-26 14:33 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 14:34 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-26 14:49 -0700
Re: In the Binary Tree there ... j4n bur53 <janburse@fastmail.fm> - 2018-06-26 23:54 +0200
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-26 14:00 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-26 18:28 -0500
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-27 06:49 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-27 07:05 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-27 07:44 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-27 07:53 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-27 08:07 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-27 08:39 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-27 18:24 -0500
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-28 06:56 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-28 07:00 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-28 15:58 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-29 06:23 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-29 18:40 -0500
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-30 06:57 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-30 09:37 -0500
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-26 05:41 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-26 06:33 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-26 06:39 -0700
Re: In the Binary Tree there ... Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-06-26 07:05 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-06-26 16:38 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-26 09:13 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-26 18:32 -0500
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-06-27 15:00 +0100
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-26 18:31 -0500
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-26 20:56 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-27 18:25 -0500
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-24 20:16 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-24 20:21 -0700
Re: In the Binary Tree there ... j4n bur53 <janburse@fastmail.fm> - 2018-06-22 17:33 +0200
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 08:42 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 08:48 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 09:03 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 09:12 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 09:41 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 09:50 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 09:56 -0700
Re: In the Binary Tree there ... j4n bur53 <janburse@fastmail.fm> - 2018-06-22 19:16 +0200
Re: In the Binary Tree there ... j4n bur53 <janburse@fastmail.fm> - 2018-06-22 19:23 +0200
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-22 08:58 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 09:00 -0700
Re: In the Binary Tree there ... j4n bur53 <janburse@fastmail.fm> - 2018-06-22 22:28 +0200
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-22 18:57 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-22 19:27 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:28 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-23 10:04 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-23 10:51 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-23 11:02 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-23 11:04 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-23 11:10 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-23 11:52 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-23 21:37 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-24 03:42 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 11:39 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-24 11:55 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 12:02 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-24 11:46 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 12:00 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-24 12:39 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 12:58 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-24 13:09 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-24 13:11 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 14:13 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-24 14:34 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 14:58 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-24 15:02 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 15:12 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-24 15:14 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 15:30 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-24 16:01 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-24 22:00 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 20:28 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:29 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 20:31 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:33 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 20:34 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:35 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 20:36 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:39 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-22 20:41 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:45 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-22 22:16 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:21 -0700
Re: In the Binary Tree there ... j4n bur53 <janburse@fastmail.fm> - 2018-06-23 05:47 +0200
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:50 -0700
Re: In the Binary Tree there ... j4n bur53 <janburse@fastmail.fm> - 2018-06-23 05:54 +0200
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-06-22 20:59 -0700
Re: In the Binary Tree there ... j4n bur53 <janburse@fastmail.fm> - 2018-06-23 06:02 +0200
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-06-24 22:58 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-25 02:42 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-06-25 22:50 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-26 04:12 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-06-26 23:05 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-27 06:42 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-27 18:26 -0500
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-28 06:53 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-28 16:00 -0500
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-28 14:17 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-28 14:55 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-06-29 02:04 +0200
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-28 19:36 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-29 06:30 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-29 18:45 -0500
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-30 06:57 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-30 07:03 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-30 09:42 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-30 14:41 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-06-30 22:45 -0500
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-30 21:56 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-01 04:14 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-01 12:57 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-01 13:05 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-02 05:04 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-02 08:04 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-02 05:04 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-02 06:13 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-02 06:39 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-02 06:54 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-02 06:59 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-02 07:34 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-02 08:25 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-02 10:22 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-02 10:35 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-02 11:38 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-02 11:44 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-02 18:13 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-02 11:38 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-01 20:37 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-02 11:39 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-02 18:50 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-03 05:49 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-03 19:26 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-04 04:26 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-04 20:31 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-05 03:50 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-05 06:22 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-05 14:17 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-05 17:24 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-06 03:38 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-06 18:23 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-07 03:25 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-07 16:41 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-08 05:20 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-08 21:42 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-09 05:09 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-09 18:40 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-10 01:47 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-10 18:26 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 05:48 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-11 11:21 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 09:53 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-11 17:06 -0500
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-11 21:50 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-12 14:51 -0500
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-12 13:22 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-12 20:43 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-13 10:54 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-13 04:17 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-13 12:34 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-13 04:49 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-13 04:51 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-13 05:06 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-13 15:17 +0200
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-13 04:46 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-13 14:38 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-13 14:46 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-13 14:56 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-13 15:23 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-13 15:15 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-13 15:39 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-14 05:14 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-14 06:52 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-14 06:54 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-14 06:58 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-14 09:52 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-16 15:47 +0100
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-24 22:48 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-13 12:03 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-13 22:19 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-13 04:41 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-12 05:49 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-12 14:53 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-13 04:41 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-14 15:57 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-15 04:38 -0700
Re: In the Binary Tree there ... jrennenkampff@googlemail.com - 2018-07-15 05:39 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-15 06:30 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-15 15:32 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-15 22:06 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-16 05:00 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-16 07:51 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-16 06:12 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-16 15:58 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-17 05:27 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-18 21:03 -0500
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-19 06:10 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-19 22:03 -0500
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-20 03:15 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-20 05:12 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-20 07:30 -0500
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-20 13:52 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-20 14:20 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-11 21:38 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-11 21:44 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-11 06:45 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 08:13 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-15 01:44 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-15 04:38 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-15 21:10 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-15 21:21 -0700
Re: In the Binary Tree there ... FromTheRafters <erratic@nomail.afraid.org> - 2018-07-16 09:21 -0400
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-16 06:48 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-16 13:35 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-17 05:20 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-17 05:29 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-17 10:53 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-17 11:31 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-17 22:39 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-17 22:47 -0700
Re: In the Binary Tree there ... FromTheRafters <erratic@nomail.afraid.org> - 2018-07-18 06:17 -0400
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 09:16 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-18 06:12 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-18 17:11 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-19 05:37 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-20 12:20 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-20 05:03 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-20 14:33 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-20 11:41 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-21 20:58 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-22 06:16 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-22 15:49 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-23 06:21 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-23 14:52 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-23 10:12 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-23 18:38 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-24 06:58 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-24 13:47 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-25 04:26 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-25 14:02 +0100
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-25 06:20 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-25 16:41 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-25 09:45 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-25 19:42 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-26 03:52 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-26 14:36 +0100
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-26 07:26 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-26 15:36 +0100
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-26 09:38 -0700
Re: In the Binary Tree there ... FredJeffries <fredjeffries@gmail.com> - 2018-07-26 11:37 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-26 12:21 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-26 14:35 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-26 14:41 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-26 15:13 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-26 16:42 +0200
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-25 12:35 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-26 03:50 -0700
Re: In the Binary Tree there ... "K_h" <KHolmes@SX729.com> - 2018-07-24 19:03 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-24 20:23 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-25 04:35 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-25 13:45 +0200
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-25 06:24 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-25 15:29 +0200
Re: In the Binary Tree there ... Jürgen R. <jurgenr@web.de> - 2018-07-25 21:51 +0200
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-25 12:57 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-26 03:47 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-26 12:58 +0200
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-26 05:32 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-26 14:36 +0200
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-26 14:40 +0200
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-26 06:56 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-26 07:28 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-26 07:32 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-26 14:24 +0100
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-26 07:26 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-26 15:43 +0100
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-26 09:38 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-26 18:46 +0200
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-26 18:50 +0200
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-26 05:36 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-26 14:42 +0200
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-26 07:30 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-26 16:41 +0200
Re: In the Binary Tree there ... jrennenkampff@googlemail.com - 2018-07-27 05:34 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-27 06:43 -0700
Re: In the Binary Tree there ... jrennenkampff@googlemail.com - 2018-07-29 04:14 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-25 14:02 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-25 14:13 -0700
Re: In the Binary Tree there ... "K_h" <KHolmes@SX729.com> - 2018-07-26 11:33 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-27 04:17 -0700
Re: In the Binary Tree there ... "K_h" <KHolmes@SX729.com> - 2018-07-27 12:03 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-27 13:03 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-28 05:58 -0700
Re: In the Binary Tree there ... Zeit Geist <Tucsondrew@me.com> - 2018-07-28 14:15 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-29 04:06 -0700
Re: In the Binary Tree there ... Zeit Geist <Tucsondrew@me.com> - 2018-07-29 12:27 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-30 01:35 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-30 04:39 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-30 07:32 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-30 07:39 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-30 07:46 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-30 09:09 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-30 18:15 +0200
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-30 11:36 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-30 11:45 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-30 11:48 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-30 12:03 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-30 12:11 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-31 04:05 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-31 04:48 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-31 05:25 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-31 10:02 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-31 12:47 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-31 12:59 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-31 14:01 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-31 14:27 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-31 15:10 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-31 15:51 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-31 17:14 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-31 20:44 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-31 14:45 +0200
Re: In the Binary Tree there ... "K_h" <KHolmes@SX729.com> - 2018-07-28 16:12 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-29 04:40 -0700
Re: In the Binary Tree there ... FredJeffries <fredjeffries@gmail.com> - 2018-07-29 11:55 -0700
Re: In the Binary Tree there ... "K_h" <KHolmes@SX729.com> - 2018-07-29 22:19 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-30 04:38 -0700
Re: In the Binary Tree there ... "K_h" <KHolmes@SX729.com> - 2018-07-30 13:48 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-31 04:15 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-31 14:42 +0200
Re: In the Binary Tree there ... "K_h" <KHolmes@SX729.com> - 2018-07-31 20:52 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-08-01 03:50 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-08-01 22:14 -0700
Re: In the Binary Tree there ... FredJeffries <fredjeffries@gmail.com> - 2018-08-02 16:29 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-08-02 16:35 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-08-02 22:55 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-08-03 11:59 +0200
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-08-03 09:46 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-08-03 11:04 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-08-01 22:10 -0700
Re: In the Binary Tree there ... Zeit Geist <Tucsondrew@me.com> - 2018-07-27 14:38 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-07-28 05:44 -0700
Re: In the Binary Tree there ... Zeit Geist <Tucsondrew@me.com> - 2018-07-28 14:12 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-29 04:06 -0700
Re: In the Binary Tree there ... Zeit Geist <Tucsondrew@me.com> - 2018-07-29 12:29 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-16 05:05 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-16 05:12 -0700
Re: In the Binary Tree there ... jrennenkampff@googlemail.com - 2018-07-16 05:27 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-16 06:07 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-16 23:08 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-17 06:24 -0700
Re: In the Binary Tree there ... Mike Hart <gmoralesor@gmail.com> - 2018-07-17 08:42 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-17 10:52 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-17 16:25 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-17 23:28 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 05:16 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 05:29 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 09:45 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 12:12 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 12:17 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 12:30 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 12:46 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 12:47 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 12:59 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 13:27 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 13:30 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 13:43 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 14:27 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 14:31 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 15:10 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 12:42 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-05 20:51 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-06 03:46 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-06 13:02 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-06 18:25 -0500
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-06 16:29 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-06-27 22:27 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-28 06:52 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-28 14:25 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-28 16:21 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-29 06:30 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-06-30 21:54 -0700
Re: In the Binary Tree there ... FredJeffries <fredjeffries@gmail.com> - 2018-07-01 11:37 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-02 13:10 -0700
Re: In the Binary Tree there ... FredJeffries <fredjeffries@gmail.com> - 2018-07-02 14:38 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-02 14:47 -0700
Re: In the Binary Tree there ... FredJeffries <fredjeffries@gmail.com> - 2018-07-02 18:06 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-21 15:22 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-06-28 22:37 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-29 06:36 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-29 07:45 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-29 07:52 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-29 12:57 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-29 16:56 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-06-29 17:01 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-29 18:23 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-06-30 14:47 +0200
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-30 09:46 -0700
Re: In the Binary Tree there ... transfinity01@gmail.com - 2018-06-30 07:13 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-03 02:09 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-03 06:03 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-03 15:11 +0200
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-04 01:50 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-04 04:30 -0700
Re: In the Binary Tree there ... jrennenkampff@googlemail.com - 2018-07-04 05:06 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-05 03:45 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-05 20:53 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-05 20:58 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-06 03:46 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-06 13:06 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-05 01:51 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-05 03:54 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-05 04:55 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-05 14:20 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-06 02:31 +0200
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-06 02:18 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-06 03:54 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-04 20:37 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-05 04:04 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-05 04:26 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-05 14:10 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-05 16:26 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-06 03:42 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-06 08:03 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-06 11:40 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-06 12:03 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-06 14:24 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-06 15:18 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-06 15:41 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-06 15:59 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-07 03:42 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-07 05:40 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-07 06:18 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-07 06:52 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-07 07:03 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-07 10:21 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-07 12:18 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-08 05:09 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-08 07:53 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-08 08:17 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-08 17:29 +0200
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-08 09:07 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-08 09:50 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-08 10:45 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-09 04:58 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-09 14:31 +0200
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-09 07:42 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-09 08:45 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-09 08:59 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-09 09:21 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-10 01:47 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-10 08:11 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-10 13:01 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 05:37 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-11 14:00 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-10 13:24 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 05:57 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-11 07:02 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-11 07:19 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 08:15 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-11 08:46 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 09:54 -0700
Re: In the Binary Tree there ... wpihughes@gmail.com - 2018-07-11 10:31 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-09 10:12 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-10 01:54 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-10 15:33 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-10 07:45 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-10 16:50 +0200
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-10 08:00 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-10 17:05 +0200
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-10 16:11 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-10 08:22 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-10 08:34 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-11 19:06 +0100
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-10 16:58 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-10 09:03 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 05:34 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-11 15:29 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 08:31 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-11 17:02 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-11 09:44 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-17 13:56 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-17 11:04 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-17 19:38 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-17 11:52 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-18 16:53 +0100
Re: In the Binary Tree there ... FredJeffries <fredjeffries@gmail.com> - 2018-07-18 09:46 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-18 10:05 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-18 18:54 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-18 11:16 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 11:42 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-18 13:14 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-19 02:02 +0200
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-19 05:28 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-19 13:40 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-20 11:54 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-20 04:41 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-20 13:01 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-20 10:27 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-21 20:49 +0100
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-22 23:51 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-23 14:45 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-20 05:52 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-20 14:36 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-20 11:44 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-20 11:56 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-20 13:25 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-20 13:33 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-21 21:11 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-22 06:07 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-22 07:42 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-18 16:00 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-18 19:17 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-18 19:19 -0700
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-18 19:23 -0700
Re: In the Binary Tree there ... "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-07-19 22:05 -0500
Re: In the Binary Tree there ... Julio Di Egidio <julio@diegidio.name> - 2018-07-20 03:12 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-18 05:58 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 06:19 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-18 06:28 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-19 05:28 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-19 13:42 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-19 13:55 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-19 14:05 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-19 14:20 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-19 15:08 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-19 15:15 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-20 05:43 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-20 13:36 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-18 17:04 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-19 05:33 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-20 12:08 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-20 06:14 -0700
Re: In the Binary Tree there ... bursejan@gmail.com - 2018-07-20 06:21 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-20 16:04 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-20 11:53 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-21 21:21 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-22 05:59 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-22 15:39 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-23 06:21 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-23 15:10 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-23 10:19 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-08 09:51 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-08 10:50 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-08 13:38 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-08 14:03 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-08 15:19 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-09 04:58 -0700
Re: In the Binary Tree there ... "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-07-09 22:28 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-10 13:34 -0700
Re: In the Binary Tree there ... "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-07-10 14:47 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-09 01:34 -0700
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-09 04:59 -0700
Re: In the Binary Tree there ... Zelos Malum <zelos.malum@gmail.com> - 2018-07-11 06:44 -0700
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-07 01:58 +0200
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-07 03:27 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-06 11:32 +0100
Re: In the Binary Tree there ... WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-07-06 03:53 -0700
Re: In the Binary Tree there ... Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-07-06 12:27 +0100
Re: In the Binary Tree there ... Python <python@python.invalid> - 2018-07-05 14:08 +0200
Page 31 of 32 — ← Prev page 1 … 29 30 [31] 32 Next page →
| From | bursejan@gmail.com |
|---|---|
| Date | 2018-07-19 13:55 -0700 |
| Message-ID | <75fd37e3-47ba-4c0f-82d8-08b63741be1c@googlegroups.com> |
| In reply to | #418547 |
If you use a desired level of precision,
you simply get another real number x', such that:
|x - x'| < e if you look at absolute error
|x - x'|
|------| < e if you look at relative error
| x |
But a real number is not a multitude of objects,
with varying precision. Not automatically,
only if the limit of these precision objects
x'1, x'2, x'3, ... is the real number itself:
lim n->oo x'n = x
Not very helpful...
An infinite normalized sequence, can be
directly taken as a real number, so to speak
with "infinite" precision. And then you might
step over real numbers (in mathematics) that do
not have effective (on the computer) precision
approximations. For example the Specker real number:
https://en.wikipedia.org/wiki/Specker_sequence
Am Donnerstag, 19. Juli 2018 22:42:20 UTC+2 schrieb Chris M. Thomasson:
> On 7/19/2018 5:28 AM, WM wrote:
> > Am Mittwoch, 18. Juli 2018 15:19:19 UTC+2 schrieb burs...@gmail.com:
> >> The real number is defined from sequence not
> >> from formula.
> >
> > A definition needs an end signal. An infinite sequence has not. So it cannot define a real number.
>
> It can be used to help define a real number using a desired level of
> precision.
>
>
> > But even that mistaken view can be contradicted since in the Binary Tree there are only countably many different infinite sequences / paths.
[toc] | [prev] | [next] | [standalone]
| From | bursejan@gmail.com |
|---|---|
| Date | 2018-07-19 14:05 -0700 |
| Message-ID | <f7210d13-a4e7-4655-ba8c-6f1a1011bbb2@googlegroups.com> |
| In reply to | #418548 |
Not very helpful, because (x'1, x'2, x'3, ...) is again an infinite sequence. So you didn't get rid of infinite sequences. Am Donnerstag, 19. Juli 2018 22:56:08 UTC+2 schrieb burs...@gmail.com: > If you use a desired level of precision, > you simply get another real number x', such that: > > |x - x'| < e if you look at absolute error > > |x - x'| > |------| < e if you look at relative error > | x | > > But a real number is not a multitude of objects, > with varying precision. Not automatically, > > only if the limit of these precision objects > x'1, x'2, x'3, ... is the real number itself: > > lim n->oo x'n = x > > Not very helpful... > > An infinite normalized sequence, can be > directly taken as a real number, so to speak > > with "infinite" precision. And then you might > step over real numbers (in mathematics) that do > > not have effective (on the computer) precision > approximations. For example the Specker real number: > > https://en.wikipedia.org/wiki/Specker_sequence > > Am Donnerstag, 19. Juli 2018 22:42:20 UTC+2 schrieb Chris M. Thomasson: > > On 7/19/2018 5:28 AM, WM wrote: > > > Am Mittwoch, 18. Juli 2018 15:19:19 UTC+2 schrieb burs...@gmail.com: > > >> The real number is defined from sequence not > > >> from formula. > > > > > > A definition needs an end signal. An infinite sequence has not. So it cannot define a real number. > > > > It can be used to help define a real number using a desired level of > > precision. > > > > > > > But even that mistaken view can be contradicted since in the Binary Tree there are only countably many different infinite sequences / paths.
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| From | "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> |
|---|---|
| Date | 2018-07-19 14:20 -0700 |
| Message-ID | <piqvan$muc$1@dont-email.me> |
| In reply to | #418550 |
On 7/19/2018 2:05 PM, bursejan@gmail.com wrote: > Not very helpful, because (x'1, x'2, x'3, ...) > is again an infinite sequence. So you didn't > > get rid of infinite sequences. [...] I was not trying to get rid of infinite sequences.
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-07-19 15:08 -0700 |
| Message-ID | <4e51bd60-cf65-4e8d-ba64-1537357edf40@googlegroups.com> |
| In reply to | #418552 |
Its much easier in the binary tree. The branches can
be viewed as subsets of N. No need to deal with
real numbers.
So why is there no end signal? Because some subsets
of N are infinite. And a tree has a very special
property, namely, a finite subset can be view
as a branch which has first the finite pattern
of the subset some 0 and 1, and the infinitely
many zeros 0....
So a finite subset p is a special branch:
*
\ some 0 and 1
+-------------------------- p
all zeros
So a tree has now the proberty that an infinite
union of ascending finite sets p1, p2, ..., exists
in the form of an infinite set q which is also a branch.
Visually its very easy, the ascending finite sets are:
*
\
+-----+------------------------------------ p1
\
+--------+------------------------- p2
\
+-----+----------------- p3
\
+---- .
.
.
the infinite union is simply this branch:
*
\
+-----+
\
+--------+
\
+-----+
\
+------ .
.
. q
Real numbers are similar. But lets stick to P(N)
and spot the error of an end signal in the logic
of Augsburg Crank institute.
What is the end signal in q? Some horn sounding
by Volkswagen Omlette? The last audio of the Titanic?
The church bell from Augsburg?
Am Donnerstag, 19. Juli 2018 23:20:29 UTC+2 schrieb Chris M. Thomasson:
> On 7/19/2018 2:05 PM, bursejan@gmail.com wrote:
> > Not very helpful, because (x'1, x'2, x'3, ...)
> > is again an infinite sequence. So you didn't
> >
> > get rid of infinite sequences.
> [...]
>
> I was not trying to get rid of infinite sequences.
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-07-19 15:15 -0700 |
| Message-ID | <7f2b110c-8b2c-4eb7-9ae2-4ab351898b38@googlegroups.com> |
| In reply to | #418553 |
Whats this end-signal? AP brain fartos infinity border 10^604? The number of electrons in the universe? Hells Bells by AC/DC? AC/DC - Hells Bells (Official Video) https://www.youtube.com/watch?v=etAIpkdhU9Q In mathematics and infinite sequence and branches of the bineary tree do not have an end-signal. And they are the object of Cantors theorem. And not some definable subsets of N. That definable subsets of N are incomplete, is already seen by the example I gave. Here I simply equated a definable subset of N with finite subset of N. But a tree is much richer. A tree and P(A) has this property guarded by union axiom of set theory: X subset P(A) => U X in P(A) /* 1 */ The union axiom doesn't say it directly: https://en.wikipedia.org/wiki/Axiom_of_union Homework: Prove /* 1 */ in FOL+ZFC. Or maybe use Dan Christensens DC Proof to prove it. Am Freitag, 20. Juli 2018 00:08:23 UTC+2 schrieb burs...@gmail.com: > Its much easier in the binary tree. The branches can > be viewed as subsets of N. No need to deal with > real numbers. > > So why is there no end signal? Because some subsets > of N are infinite. And a tree has a very special > property, namely, a finite subset can be view > > as a branch which has first the finite pattern > of the subset some 0 and 1, and the infinitely > many zeros 0.... > > So a finite subset p is a special branch: > > > * > \ some 0 and 1 > +-------------------------- p > all zeros > > So a tree has now the proberty that an infinite > union of ascending finite sets p1, p2, ..., exists > in the form of an infinite set q which is also a branch. > > Visually its very easy, the ascending finite sets are: > > * > \ > +-----+------------------------------------ p1 > \ > +--------+------------------------- p2 > \ > +-----+----------------- p3 > \ > +---- . > . > . > > the infinite union is simply this branch: > > * > \ > +-----+ > \ > +--------+ > \ > +-----+ > \ > +------ . > . > . q > > > Real numbers are similar. But lets stick to P(N) > and spot the error of an end signal in the logic > of Augsburg Crank institute. > > What is the end signal in q? Some horn sounding > by Volkswagen Omlette? The last audio of the Titanic? > The church bell from Augsburg? > > Am Donnerstag, 19. Juli 2018 23:20:29 UTC+2 schrieb Chris M. Thomasson: > > On 7/19/2018 2:05 PM, bursejan@gmail.com wrote: > > > Not very helpful, because (x'1, x'2, x'3, ...) > > > is again an infinite sequence. So you didn't > > > > > > get rid of infinite sequences. > > [...] > > > > I was not trying to get rid of infinite sequences.
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-07-20 05:43 -0700 |
| Message-ID | <a4822fb4-2849-434f-8c29-4642d8c65322@googlegroups.com> |
| In reply to | #418547 |
Am Donnerstag, 19. Juli 2018 22:42:20 UTC+2 schrieb Chris M. Thomasson: > On 7/19/2018 5:28 AM, WM wrote: > > Am Mittwoch, 18. Juli 2018 15:19:19 UTC+2 schrieb burs...@gmail.com: > >> The real number is defined from sequence not > >> from formula. > > > > A definition needs an end signal. An infinite sequence has not. So it cannot define a real number. > > It can be used to help define a real number using a desired level of > precision. You will never define more than a rational interval. Never pi. Regards, WM
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| From | "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> |
|---|---|
| Date | 2018-07-20 13:36 -0700 |
| Message-ID | <pith46$1d0$1@dont-email.me> |
| In reply to | #418616 |
On 7/20/2018 5:43 AM, WM wrote: > Am Donnerstag, 19. Juli 2018 22:42:20 UTC+2 schrieb Chris M. Thomasson: >> On 7/19/2018 5:28 AM, WM wrote: >>> Am Mittwoch, 18. Juli 2018 15:19:19 UTC+2 schrieb burs...@gmail.com: >>>> The real number is defined from sequence not >>>> from formula. >>> >>> A definition needs an end signal. An infinite sequence has not. So it cannot define a real number. >> >> It can be used to help define a real number using a desired level of >> precision. > > You will never define more than a rational interval. Never pi. We can define a finite snapshot of a portion of pi. Convergents of continued fractions can help define a rational that can describe any number up to a finite level of precision. real = 577 / 408 = 1.41421 wrt 5 digits of precision. Any more precision, and it differs from the target irrational at sqrt(2).
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2018-07-18 17:04 +0100 |
| Message-ID | <fwe601ccyyn.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #418324 |
WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > Am Dienstag, 17. Juli 2018 20:40:08 UTC+2 schrieb Alan Smaill: > >> > The reals in the list are only rationals, since they must be >> > represented by their digits (for this proof) and that cannot yield >> > irrationals. >> >> Wrong; a finitely specified algorithm can very well supply a potentially >> infinite stream of digits: for example for the square root of 2. >> And you accept already that this is in fact can be shown to be an >> irrational number. > > But the list contains only the digit sequence since the diagonal > argument requires the digit a_nn. That is not the situation I specified. The whole figure has a single finitely given specification. The specification is such that mth digit of the nth entry can be shown to be assigned to a unique digit. So, obviously, the figure is not given directly by digits. > Further, yes I accept that the algorithm can supply every digit. But > every digit belongs to a rational approximation. The complete digit > sequence is not possible to give. Therefore I said that the algorithm > or formule is the number. You think I am saying something different?? > "Formula gives Sequence". The inversion "Sequence gives Formula" is > false. But the list contains only the sequence, so it does not contain > the number. Or put in other words: It is impossible from the list > entry to find the number represented. So what? If you have a single algorithmic description of the grid, then you can use that to give a single algorithmic description of the diagonal. There is no going from the list to the number involved. > > Regards, WM > > -- Alan Smaill
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-07-19 05:33 -0700 |
| Message-ID | <0457319c-397c-4fd2-8a94-c9e5d407e323@googlegroups.com> |
| In reply to | #418371 |
Am Mittwoch, 18. Juli 2018 18:05:07 UTC+2 schrieb Alan Smaill: > WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > > > Am Dienstag, 17. Juli 2018 20:40:08 UTC+2 schrieb Alan Smaill: > > > >> > The reals in the list are only rationals, since they must be > >> > represented by their digits (for this proof) and that cannot yield > >> > irrationals. > >> > >> Wrong; a finitely specified algorithm can very well supply a potentially > >> infinite stream of digits: for example for the square root of 2. > >> And you accept already that this is in fact can be shown to be an > >> irrational number. > > > > But the list contains only the digit sequence since the diagonal > > argument requires the digit a_nn. > > That is not the situation I specified. The whole figure has a single > finitely given specification. The specification is such that > mth digit of the nth entry can be shown to be assigned to a unique digit. > So, obviously, the figure is not given directly by digits. But the entries are. > > > Further, yes I accept that the algorithm can supply every digit. But > > every digit belongs to a rational approximation. The complete digit > > sequence is not possible to give. Therefore I said that the algorithm > > or formule is the number. > > You think I am saying something different?? No, I have seen that you agree. But Cantor's list needs numbers defined by digits, for instance the diagonal. And of course every irrational you wish to use there an an entry. > > > "Formula gives Sequence". The inversion "Sequence gives Formula" is > > false. But the list contains only the sequence, so it does not contain > > the number. Or put in other words: It is impossible from the list > > entry to find the number represented. > > So what? If you have a single algorithmic description of the grid, You mean that every entry is defined by a formula like in the list 0.1 0.11 0.111 ... ? Then the list and also its diagonal belong to the countable set of finite definitions. > then you can use that to give a single algorithmic description > of the diagonal. and prove it is a member of the countable set of all finite definitions. Regards, WM
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2018-07-20 12:08 +0100 |
| Message-ID | <fwelga6nozt.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #418502 |
WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > Am Mittwoch, 18. Juli 2018 18:05:07 UTC+2 schrieb Alan Smaill: >> WM <wolfgang.mueckenheim@hs-augsburg.de> writes: >> >> > Am Dienstag, 17. Juli 2018 20:40:08 UTC+2 schrieb Alan Smaill: >> > >> >> > The reals in the list are only rationals, since they must be >> >> > represented by their digits (for this proof) and that cannot yield >> >> > irrationals. >> >> >> >> Wrong; a finitely specified algorithm can very well supply a potentially >> >> infinite stream of digits: for example for the square root of 2. >> >> And you accept already that this is in fact can be shown to be an >> >> irrational number. >> > >> > But the list contains only the digit sequence since the diagonal >> > argument requires the digit a_nn. >> >> That is not the situation I specified. The whole figure has a single >> finitely given specification. The specification is such that >> mth digit of the nth entry can be shown to be assigned to a unique digit. >> So, obviously, the figure is not given directly by digits. > > But the entries are. No, they are not. Where do ypu get that from? As I said at the start, this is all set up using *your* terminology (as far as I understand it). It even says immeediately above "The whole figure has a single finitely given specification". In that case, you can work out what the definition of a particular row from the overall definition, given a half-sensible definition language. >> > Further, yes I accept that the algorithm can supply every digit. But >> > every digit belongs to a rational approximation. The complete digit >> > sequence is not possible to give. Therefore I said that the algorithm >> > or formule is the number. >> >> You think I am saying something different?? > > No, I have seen that you agree. But Cantor's list needs numbers > defined by digits, for instance the diagonal. And of course every > irrational you wish to use there an an entry. On the basis of a finite definition only. >> > "Formula gives Sequence". The inversion "Sequence gives Formula" is >> > false. But the list contains only the sequence, so it does not contain >> > the number. Or put in other words: It is impossible from the list >> > entry to find the number represented. >> >> So what? If you have a single algorithmic description of the grid, > > You mean that every entry is defined by a formula like in the list > > 0.1 > 0.11 > 0.111 > ... > ? > Then the list and also its diagonal belong to the countable set of > finite definitions. No, I do not know what else is in that diagram. Can you give a formula D(x,y) where D(x,y) is either 0 or 1, and indicates which digit appears as the yth digit of the xth line? >> then you can use that to give a single algorithmic description >> of the diagonal. > > and prove it is a member of the countable set of all finite definitions. Come now, no proof needed to say that the set of definitions is countable. Try proving that the antidiagonal differs from each entry in the original diagram, in the same way that sqrt(2) =/= n/m, regardless of what naturals n,m are. This is not a claim about cardinality, please do not jump to that conclusion. > Regards, WM -- Alan Smaill
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-07-20 06:14 -0700 |
| Message-ID | <b032e454-1d69-47c8-aa22-fa2978a9dc5d@googlegroups.com> |
| In reply to | #418604 |
Am Freitag, 20. Juli 2018 13:10:07 UTC+2 schrieb Alan Smaill: > WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > >> > Further, yes I accept that the algorithm can supply every digit. But > >> > every digit belongs to a rational approximation. The complete digit > >> > sequence is not possible to give. Therefore I said that the algorithm > >> > or formule is the number. > >> > >> You think I am saying something different?? > > > > No, I have seen that you agree. But Cantor's list needs numbers > > defined by digits, for instance the diagonal. And of course every > > irrational you wish to use there an an entry. > > On the basis of a finite definition only. Is the following example possible?: Row n contains 1/sqrt(n). > > > > You mean that every entry is defined by a formula like in the list > > > > 0.1 > > 0.11 > > 0.111 > > ... > > ? > > Then the list and also its diagonal belong to the countable set of > > finite definitions. > > No, I do not know what else is in that diagram. "..." say: and so on. > Can you give a formula D(x,y) where D(x,y) is either 0 or 1, > and indicates which digit appears as the yth digit of the xth line? After the decimal point: D(x, y) = 1 for y =< x, otherwise 0. > > >> then you can use that to give a single algorithmic description > >> of the diagonal. > > > > and prove it is a member of the countable set of all finite definitions. > > Come now, no proof needed to say that the set of definitions is countable. The set of finite strings is countable. Definitions are a subset. > > Try proving that the antidiagonal differs from each entry in the > original diagram, in the same way that sqrt(2) =/= n/m, regardless of > what naturals n,m are. For my simple example the case is obvious. The antidagonal of 0.000... 0.1000... 0.11000... 0.111000... ... can be taken as 0.111... It is only then infinite, when the list has infinitely many lines and infinitely many columns. But then the number 0.111... must be in the list already, since otherwise infinitely many columns must contain entries ending with infinitely many zeros and the diagonal will not cover all columns. Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-07-20 06:21 -0700 |
| Message-ID | <abd52ab1-e041-46d3-8b59-76061c67239d@googlegroups.com> |
| In reply to | #418621 |
Nope, |N| < |P(N)|, so its not possible to list
infinite bit sequences. There is no listing
f : N -> P(N), which is surjective.
Because for any such listing, the diagonal:
d = { x in N | x not in f(x) }
will be missing.
Am Freitag, 20. Juli 2018 15:14:09 UTC+2 schrieb WM:
> Am Freitag, 20. Juli 2018 13:10:07 UTC+2 schrieb Alan Smaill:
> > WM <wolfgang.mueckenheim@hs-augsburg.de> writes:
>
>
> > >> > Further, yes I accept that the algorithm can supply every digit. But
> > >> > every digit belongs to a rational approximation. The complete digit
> > >> > sequence is not possible to give. Therefore I said that the algorithm
> > >> > or formule is the number.
> > >>
> > >> You think I am saying something different??
> > >
> > > No, I have seen that you agree. But Cantor's list needs numbers
> > > defined by digits, for instance the diagonal. And of course every
> > > irrational you wish to use there an an entry.
> >
> > On the basis of a finite definition only.
>
> Is the following example possible?: Row n contains 1/sqrt(n).
>
>
> > >
> > > You mean that every entry is defined by a formula like in the list
> > >
> > > 0.1
> > > 0.11
> > > 0.111
> > > ...
> > > ?
> > > Then the list and also its diagonal belong to the countable set of
> > > finite definitions.
> >
> > No, I do not know what else is in that diagram.
>
> "..." say: and so on.
>
> > Can you give a formula D(x,y) where D(x,y) is either 0 or 1,
> > and indicates which digit appears as the yth digit of the xth line?
>
> After the decimal point: D(x, y) = 1 for y =< x, otherwise 0.
> >
> > >> then you can use that to give a single algorithmic description
> > >> of the diagonal.
> > >
> > > and prove it is a member of the countable set of all finite definitions.
> >
> > Come now, no proof needed to say that the set of definitions is countable.
> The set of finite strings is countable. Definitions are a subset.
> >
> > Try proving that the antidiagonal differs from each entry in the
> > original diagram, in the same way that sqrt(2) =/= n/m, regardless of
> > what naturals n,m are.
>
> For my simple example the case is obvious. The antidagonal of
>
> 0.000...
> 0.1000...
> 0.11000...
> 0.111000...
> ...
>
> can be taken as 0.111...
>
> It is only then infinite, when the list has infinitely many lines and infinitely many columns. But then the number 0.111... must be in the list already, since otherwise infinitely many columns must contain entries ending with infinitely many zeros and the diagonal will not cover all columns.
>
> Regards, WM
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2018-07-20 16:04 +0100 |
| Message-ID | <fwefu0elzik.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #418621 |
WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > Am Freitag, 20. Juli 2018 13:10:07 UTC+2 schrieb Alan Smaill: >> WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > > >> >> > Further, yes I accept that the algorithm can supply every digit. But >> >> > every digit belongs to a rational approximation. The complete digit >> >> > sequence is not possible to give. Therefore I said that the algorithm >> >> > or formule is the number. >> >> >> >> You think I am saying something different?? >> > >> > No, I have seen that you agree. But Cantor's list needs numbers >> > defined by digits, for instance the diagonal. And of course every >> > irrational you wish to use there an an entry. >> >> On the basis of a finite definition only. > > Is the following example possible?: Row n contains 1/sqrt(n). If you spell that out algorithically, yes. >> > >> > You mean that every entry is defined by a formula like in the list >> > >> > 0.1 >> > 0.11 >> > 0.111 >> > ... >> > ? >> > Then the list and also its diagonal belong to the countable set of >> > finite definitions. >> >> No, I do not know what else is in that diagram. > > "..." say: and so on. Still ambiguous. >> Can you give a formula D(x,y) where D(x,y) is either 0 or 1, >> and indicates which digit appears as the yth digit of the xth line? > > After the decimal point: D(x, y) = 1 for y =< x, otherwise 0. Right. >> >> then you can use that to give a single algorithmic description >> >> of the diagonal. >> > >> > and prove it is a member of the countable set of all finite definitions. >> >> Come now, no proof needed to say that the set of definitions is countable. > The set of finite strings is countable. Definitions are a subset. I just said, "no proof needed". Can you read?? >> Try proving that the antidiagonal differs from each entry in the >> original diagram, in the same way that sqrt(2) =/= n/m, regardless of >> what naturals n,m are. > > For my simple example the case is obvious. The antidagonal of > > 0.000... > 0.1000... > 0.11000... > 0.111000... > ... > > can be taken as 0.111... OK. > It is only then infinite, It is potentially infinite, in exactly the same sense that the original diagram is potentially infinite. You have a finite definition, which you can work out from D above in the general case. Here AD(n) = 1, and that corresponds to a potentially infinite list with each digit 1. > when the list has infinitely many lines and > infinitely many columns. But then the number 0.111... must be in the > list already, since otherwise infinitely many columns must contain > entries ending with infinitely many zeros and the diagonal will not > cover all columns. First, the diagonal does not cover all columns, only each column (in your terms). Your subsequent comments make no sense. Your "otherwise" includes the initial situation, and the diagonal does intersect each column. 0.111... is the antidiagonal. and it likewise intersect each column (not all). And that is enough to show that 0.111... is not in the list already -- it threatens to continue in infinity but not really requires it. > > Regards, WM -- Alan Smaill
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-07-20 11:53 -0700 |
| Message-ID | <dd80b87f-21c8-41e6-9748-6c4f49b41ec5@googlegroups.com> |
| In reply to | #418630 |
Am Freitag, 20. Juli 2018 17:05:06 UTC+2 schrieb Alan Smaill: > WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > > > Is the following example possible?: Row n contains 1/sqrt(n). > > If you spell that out algorithically, yes. > > >> > > >> > You mean that every entry is defined by a formula like in the list > >> > > >> > 0.1 > >> > 0.11 > >> > 0.111 > >> > ... > >> > ? > >> Can you give a formula D(x,y) where D(x,y) is either 0 or 1, > >> and indicates which digit appears as the yth digit of the xth line? > > > > After the decimal point: D(x, y) = 1 for y =< x, otherwise 0. > > >> Come now, no proof needed to say that the set of definitions is countable. > > The set of finite strings is countable. Definitions are a subset. > > I just said, "no proof needed". > Can you read?? Sorry, I overlooked that. > > >> Try proving that the antidiagonal differs from each entry in the > >> original diagram, in the same way that sqrt(2) =/= n/m, regardless of > >> what naturals n,m are. > > > > For my simple example the case is obvious. The antidagonal of > > > > 0.000... > > 0.1000... > > 0.11000... > > 0.111000... > > ... > > > > can be taken as 0.111... > > OK. > > > It is only then infinite, > > It is potentially infinite, in exactly the same sense > that the original diagram is potentially infinite. Here I used actual infinity. > > You have a finite definition, which you can work out from D above > in the general case. Here AD(n) = 1, and that corresponds to a potentially > infinite list with each digit 1. > > > when the list has infinitely many lines and > > infinitely many columns. But then the number 0.111... must be in the > > list already, since otherwise infinitely many columns must contain > > entries ending with infinitely many zeros and the diagonal will not > > cover all columns. > > First, the diagonal does not cover all columns, only each column > (in your terms). Sorry, I am arguing about Cantor's argument. > > Your subsequent comments make no sense. They concern Cantor's proof. > Your "otherwise" includes the initial situation, and the > diagonal does intersect each column. 0.111... is the antidiagonal. > and it likewise intersect each column (not all). > > And that is enough to show that 0.111... is not in the list already -- In potential infinity 0.111... is in the list already. It is always in the next line. Regards, WM
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2018-07-21 21:21 +0100 |
| Message-ID | <fwetvosz6f5.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #418655 |
WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > Am Freitag, 20. Juli 2018 17:05:06 UTC+2 schrieb Alan Smaill: >> WM <wolfgang.mueckenheim@hs-augsburg.de> writes: >> > >> > Is the following example possible?: Row n contains 1/sqrt(n). >> >> If you spell that out algorithically, yes. >> >> >> > >> >> > You mean that every entry is defined by a formula like in the list >> >> > >> >> > 0.1 >> >> > 0.11 >> >> > 0.111 >> >> > ... >> >> > ? > >> >> Can you give a formula D(x,y) where D(x,y) is either 0 or 1, and >> >> indicates which digit appears as the yth digit of the xth line? >> > >> > After the decimal point: D(x, y) = 1 for y =< x, otherwise 0. [..] >> >> Try proving that the antidiagonal differs from each entry in the >> >> original diagram, in the same way that sqrt(2) =/= n/m, regardless >> >> of what naturals n,m are. >> > >> > For my simple example the case is obvious. The antidagonal of >> > >> > 0.000... >> > 0.1000... >> > 0.11000... >> > 0.111000... >> > ... >> > >> > can be taken as 0.111... >> >> OK. >> >> > It is only then infinite, >> >> It is potentially infinite, in exactly the same sense >> that the original diagram is potentially infinite. > > Here I used actual infinity. And I deliberately want to keep to your own potentially infinite account. Are you saying there can be no account in terms of the potentially infinite? If so, I disagree. Forget Cantor. Do you agree with the following: >> You have a finite definition, which you can work out from D above >> in the general case. Here AD(n) = 1, and that corresponds to a potentially >> infinite list with each digit 1. -- Alan Smaill
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-07-22 05:59 -0700 |
| Message-ID | <72672225-a84c-4f58-a414-4f6962ee2506@googlegroups.com> |
| In reply to | #418766 |
Am Samstag, 21. Juli 2018 22:25:05 UTC+2 schrieb Alan Smaill: > WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > > Here I used actual infinity. > > And I deliberately want to keep to your own potentially infinite > account. Sorry, that is not my invention. It used to be the general basis of mathematics. > Are you saying there can be no account > in terms of the potentially infinite? No. But it is hard to forget Cantor, in particular because in potential infinity no paradox or exciting results occur. > Forget Cantor. My aim is to show him wrong. > > Do you agree with the following: > > >> You have a finite definition, which you can work out from D above > >> in the general case. Here AD(n) = 1, and that corresponds to a potentially > >> infinite list with each digit 1. The antidiagonal is 0.111... It is always in the next line. Using potential infinity Cantor's invincible argument is defeated. Regards, WM
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2018-07-22 15:39 +0100 |
| Message-ID | <fwefu0bz659.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #418844 |
WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > Am Samstag, 21. Juli 2018 22:25:05 UTC+2 schrieb Alan Smaill: >> WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > >> > Here I used actual infinity. >> >> And I deliberately want to keep to your own potentially infinite >> account. > > Sorry, that is not my invention. It used to be the general basis of > mathematics. Obviously you did not invent it. But you advocate its use as a way out of the decadence of modern mathematics, you have been proposing definitions of "potentially infinite", etc etc. I refer to your own understanding of the potentially infinite. >> Are you saying there can be no account >> in terms of the potentially infinite? > > No. But it is hard to forget Cantor, in particular because in > potential infinity no paradox or exciting results occur. I am suggesting that a version of the diagonal argument can be carrieed through while staying inside the potentially infinite. You seem decided to change the topic at every opportunity. >> Do you agree with the following: >> >> >> You have a finite definition, which you can work out from D above >> >> in the general case. Here AD(n) = 1, and that corresponds to a >> >> potentially infinite list with each digit 1. > > The antidiagonal is 0.111... It is always in the next line. Using > potential infinity Cantor's invincible argument is defeated. OK, so the antidiagonal is 0.111... (so the constant function AD(n) = 1 gives the potentially infinite listing). But where on earth do you get "it is always in the next line .." from? Here we had agreed to assume an initial configuration where a finite definition D(n,m) is strong enough to pin down uniquely for each n,m the mth digit on the nth entry. The starting point in this particular example, according to you (looking at digits after the decimal point): D(n,m) = 1 if m < n, 0 otherwise For given n, the nth entry has digit 0 from index n onwards, so the entry is not 0.111... , so it is not in the initial diagram anywhere. This is immediate from the definition of D in this case. > > Regards, WM > > -- Alan Smaill
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-07-23 06:21 -0700 |
| Message-ID | <6cd29f90-9130-4b73-b161-b3b1e19500f6@googlegroups.com> |
| In reply to | #418849 |
Am Sonntag, 22. Juli 2018 16:40:06 UTC+2 schrieb Alan Smaill: > WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > I am suggesting that a version of the diagonal argument can be carrieed > through while staying inside the potentially infinite. I do not see a way. Consider the list 0.0 0.1 0.11 0.111 ... The antidiagonal is always in the next line. And more does not exist. > But where on earth do you get "it is always in the next line .." from? The antidiagonal of the list 0.0 0.1 0.11 0.111 is 0.1111 (when replacing 0 --> 1). This is the same number as would follow in the next line. > > Here we had agreed to assume an initial configuration where > a finite definition D(n,m) is strong enough to pin down uniquely > for each n,m the mth digit on the nth entry. Of course, for each and every, but not for all. The potetially infinite list is longer than the finite list above, but it is always finite. And always a next line will exist. > > The starting point in this particular example, > according to you (looking at digits after > the decimal point): > > D(n,m) = 1 if m < n, 0 otherwise > > For given n, the nth entry has digit 0 from index n onwards, so the > entry is not 0.111... , so it is not in the initial diagram anywhere. The entry 0.111000... is the same as the entry 0.111. Regards, WM
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2018-07-23 15:10 +0100 |
| Message-ID | <fwefu0axctp.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #418940 |
WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > Am Sonntag, 22. Juli 2018 16:40:06 UTC+2 schrieb Alan Smaill: >> WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > > >> I am suggesting that a version of the diagonal argument can be carrieed >> through while staying inside the potentially infinite. > > I do not see a way. Consider the list > > 0.0 > 0.1 > 0.11 > 0.111 > ... > > The antidiagonal is always in the next line. And more does not exist. The antidiagonal of the whole diagram is 0.111... as you well know. It is not in the list. >> But where on earth do you get "it is always in the next line .." from? > > The antidiagonal of the list > > 0.0 > 0.1 > 0.11 > 0.111 > > is 0.1111 (when replacing 0 --> 1). > > This is the same number as would follow in the next line. Different list -- irrelevant. >> Here we had agreed to assume an initial configuration where >> a finite definition D(n,m) is strong enough to pin down uniquely >> for each n,m the mth digit on the nth entry. > > Of course, for each and every, but not for all. The potetially > infinite list is longer than the finite list above, but it is always > finite. And always a next line will exist. But we can reason from the definition and prove properties of the potentially infinite collection. >> The starting point in this particular example, >> according to you (looking at digits after >> the decimal point): >> >> D(n,m) = 1 if m < n, 0 otherwise >> >> For given n, the nth entry has digit 0 from index n onwards, so the >> entry is not 0.111... , so it is not in the initial diagram anywhere. > > The entry 0.111000... is the same as the entry 0.111. So what??? Can you work out from D(n,m) = 1 if m < n, 0 otherwise that for each (not all, each) n there is some m such that D(n,m) = 0? What does that tell you about 0.111... ? > Regards, WM -- Alan Smaill
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-07-23 10:19 -0700 |
| Message-ID | <aa15a88a-e12c-4a3b-b43a-2632991fdf83@googlegroups.com> |
| In reply to | #418947 |
Am Montag, 23. Juli 2018 16:15:06 UTC+2 schrieb Alan Smaill: > WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > > > Am Sonntag, 22. Juli 2018 16:40:06 UTC+2 schrieb Alan Smaill: > >> WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > > > > > >> I am suggesting that a version of the diagonal argument can be carrieed > >> through while staying inside the potentially infinite. > > > > I do not see a way. Consider the list > > > > 0.0 > > 0.1 > > 0.11 > > 0.111 > > ... > > > > The antidiagonal is always in the next line. And more does not exist. > > The antidiagonal of the whole diagram is 0.111... as you well know. > It is not in the list. There is no whole diagram. Do you want to switch to actual infinity? > > >> But where on earth do you get "it is always in the next line .." from? > > > > The antidiagonal of the list > > > > 0.0 > > 0.1 > > 0.11 > > 0.111 > > > > is 0.1111 (when replacing 0 --> 1). > > > > This is the same number as would follow in the next line. > > Different list -- irrelevant. Relevant since every potentially infinite list is finite, growing though, but never fnished. > > >> Here we had agreed to assume an initial configuration where > >> a finite definition D(n,m) is strong enough to pin down uniquely > >> for each n,m the mth digit on the nth entry. > > > > Of course, for each and every, but not for all. The potetially > > infinite list is longer than the finite list above, but it is always > > finite. And always a next line will exist. > > But we can reason from the definition and prove properties of the > potentially infinite collection. The most important one: It is growing but never complete. The antidiagonal of every existing list is in the next line, just coming into being. > REgards, WM
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